List-I shows various functional dependencies of energy (E) on the...

List-I shows various functional dependencies of energy

(E)

on the atomic number

(Z)

. Energies associated with certain phenomena are given in List-II.\nChoose the option that describes the correct match between the entries in List-I to those in List-II.

	List-I		List-II
$(P)$	$E \propto Z^2$	$(1)$	energy of characteristic x-rays
$(Q)$	$E \propto(Z-1)^2$	$(2)$	electrostatic part of the nuclear binding energy for stable nuclei with mass numbers in the range 30 to 170
$(R)$	$E \propto Z(Z-1)$	$(3)$	energy of continuous x-rays
$(S)$	$E$ is practically independent of $Z$	$(4)$	average nuclear binding energy per nucleon for stable nuclei with mass number in the range 30 to 170
		$(5)$	energy of radiation due to electronic transitions from hydrogen-like atoms

Options

A $\mathrm{P} \rightarrow 4, \mathrm{Q} \rightarrow 3, \mathrm{R} \rightarrow 1, \mathrm{~S} \rightarrow 2$
B $\mathrm{P} \rightarrow 5, \mathrm{Q} \rightarrow 2, \mathrm{R} \rightarrow 1, \mathrm{~S} \rightarrow 4$
C $\mathrm{P} \rightarrow 5, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 2, \mathrm{~S} \rightarrow 4$
D $\mathrm{P} \rightarrow 3, \mathrm{Q} \rightarrow 2, \mathrm{R} \rightarrow 1, \mathrm{~S} \rightarrow 5$

Correct answer

C. $\mathrm{P} \rightarrow 5, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 2, \mathrm{~S} \rightarrow 4$

Step-by-step solution

(P) Energy of H -like atom is

\begin{aligned} & \mathrm{E}=-13.6 \frac{\mathrm{Z}^2}{\mathrm{n}^2} \text{ So } \\ & \mathrm{E} \propto \mathrm{Z}^2 \\ & \mathrm{P} \rightarrow(5)\end{aligned}

(Q) Energy of characteristic X-ray by moseley's correction

\begin{aligned} & E=-13.6(Z-1)^2\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right] \text{ So } \\ & E \propto(Z-1)^2 \\ & Q \rightarrow(1)\end{aligned}

(R) Electrostatics binding energy is proportional to

Z(Z-1) R \rightarrow(2)

(S) For stable nuclei with mass no. in range 30 to 170 . Binding energy per nucleon is constant \& graph is straight line

S \rightarrow(4)

Ans. (C) is correct

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